Triple-Error-Correcting BCH-Like Codes

Abstract

The binary primitive triple-error-correcting BCH code is a cyclic code of minimum distance 7 with generator polynomial having zeros $α$, $α^3$ and $α^5$ where $α$ is a primitive root of unity. The zero set of the code is said to be {1,3,5}. In the 1970's Kasami showed that one can construct similar triple-error-correcting codes using zero sets consisting of different triples than the BCH codes. Furthermore, in 2000 Chang et. al. found new triples leading to triple-error-correcting codes. In this paper a new such triple is presented. In addition a new method is presented that may be of interest in finding further such triples.

7 pages, submitted to ISIT 2009